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Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems

  • A. V. Avvakumov
  • V. F. Strizhov
  • P. N. Vabishchevich
  • A. O. VasilevEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

An automatic algorithm of time step control for solving the boundary value problems for nonstationary parabolic equations is presented. The solution is obtained using complete stable implicit schemes, and the time step is evaluated using of the explicit scheme solution. The time step evaluation formulas are derived using the estimation of the approximation error at next time step. Calculation results obtained for several neutron diffusion problems demonstrate reliability of the proposed algorithm for time step control.

Keywords

Time step selection Parabolic equation Approximation error Neutron diffusion 

Notes

Acknowledgements

This work are supported A.V. Avvakumov and V.F. Strizhov by the Russian Foundation for Basic Research #16-08-01215, P.N. Vabishchevich by the grant of the Russian Federation Government #14.Y26.31.0013 and A.O. Vasilev by the Russian Foundation for Basic Research #18-31-00315.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. V. Avvakumov
    • 1
  • V. F. Strizhov
    • 2
  • P. N. Vabishchevich
    • 2
    • 3
  • A. O. Vasilev
    • 3
    Email author
  1. 1.National Research Center Kurchatov InstituteMoscowRussia
  2. 2.Nuclear Safety Institute of RASMoscowRussia
  3. 3.North-Eastern Federal UniversityYakutskRussia

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